On large minimal blocking sets in PG(2,q)

Támas Szonyi, Antonello Cossidente, András Gács, Csaba Mengyán, Alessandro Siciliano, Zsuzsa Weiner

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17 Citations (Scopus)

Abstract

The size of large minimal blocking sets is bounded by the Bruen-Thas upper bound. The bound is sharp when q is a square. Here the bound is improved if q is a non-square. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of non-prime order. The construction can be regarded as a generalization of Buekenhout's construction of unitals. For example, if q is a cube, then our construction gives minimal blocking sets of size q4/3 + 1 or q4!3 + 2. Density results for the spectrum of minimal blocking sets in Galois planes of non-prime order is also presented. The most attractive case is when q is a square, where we show that there is a minimal blocking set for any size from the interval (Equation presented).

Original languageEnglish
Pages (from-to)25-41
Number of pages17
JournalJournal of Combinatorial Designs
Volume13
Issue number1
DOIs
Publication statusPublished - Dec 1 2005

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Keywords

  • Blocking sets
  • Density results

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Szonyi, T., Cossidente, A., Gács, A., Mengyán, C., Siciliano, A., & Weiner, Z. (2005). On large minimal blocking sets in PG(2,q). Journal of Combinatorial Designs, 13(1), 25-41. https://doi.org/10.1002/jcd.20017